?Wave-Particle DualityShow that Wien’s displacement law results from Planck’s radiation
Chapter 6, Problem 125(choose chapter or problem)
Wave-Particle Duality
Show that Wien’s displacement law results from Planck’s radiation law. (Hint: substitute \(x=h c / \lambda k T\) and write Planck’s law in the form \(I(x, T)=A x^{5} /\left(e^{x}-1\right)\), where \(A=2 \pi(k T)^{5} /\left(h^{4} c^{3}\right)\). Now, for fixed T, find the position of the maximum in I(x,T) by solving for x in the equation dI(x,T)/dx = 0.)
Text Transcription:
x=hc/lambda kT
I(x,T)=Ax^5/(e^x - 1)
A=2 pi (kT)^5/ (h^4 c^3)
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